What is causing this giraffe patterning in my fur?
The issue is you have too little particles (and too many children particles). The 'clump' setting makes the children particles follow the nearest parent particle direction. Since your parent particles are so few, they are far apart, and all the hairs in between are actually children particles leaning in the direction of the few 'parent' particles, and that's creating the pattern.
Increasing the amount of particles should solve the issue, also reduce the amount of children particles so the total amount of particles is still reasonable.
Increase this amount (I increased it to 20000):

And reduce this (I reduced it to 50):

Play around with the values to reach the result you want.